When does spatial clustering in caterpillars influence the relationship between population density and contact rates?

Abstract

While interactions in nature are inherently local, ecological models often assume homogeneity across space, allowing for generalization across systems and greater mathematical tractability. Density-dependent disease models are a prominent example that assumes homogeneous interactions, leading to the prediction that disease transmission will scale linearly with population density. In this study, we examined how larval butterfly contact rates relate to population density in the Baltimore checkerspot (Euphydryas phaeton). Our study was partly inspired by a viral disease that is transmitted horizontally among Baltimore checkerspot larvae. First, we used multi-year larvae location data across six Baltimore checkerspot populations in the eastern U.S. to test whether larval nests are spatially clustered. We then integrated these spatial data with larval movement data. We used a Correlated Random Walk (CRW) model to investigate whether heterogeneity in spatially local interactions alter the assumed linear relationship between population density and contact. We found that all populations exhibited significant spatial clustering in their habitat use. Larval movement rates were influenced by encounters with host plants, and under many movement scenarios, the scale of predicted larval movement was not sufficient to allow for the “homogeneous mixing” assumed in density dependent disease models. Therefore, relationships between population density and larval contact rates were typically non-linear. We also found that observed use of available habitat patches led to significantly greater contact rates than would occur if habitat use were spatially random. These findings strongly suggest that incorporating spatial variation in larval interactions is critical to modeling disease outcomes in this system.

Density-dependent network structuring within and across wild animal systems

“…Often, individuals are modelled as randomly moving and interacting molecules ("mass action" or "mean field"). In this conceptualisation, direct contact between two molecules is analogous to a social interaction or association; rates of such interactions are often assumed to increase with density ("density-dependent"; e.g., [15]), and/or to be homogenous in space (e.g., [10]). In reality individuals are unlikely to behave and interact randomly in space, and instead will be influenced by spatially varying factors including local density [16].…”

“…mating or fighting). While several studies have compared animal populations at different densities to demonstrate variation in social association rates among populations (e.g., [6,7]) or groups (e.g., [8][9][10]), attempts to identify such density effects within continuous populations of individuals are rarer (but see [11][12][13][14]), and their findings have never been synthesised or compared. We therefore have an incomplete understanding of how density, as a fundamental ecological parameter, determines socio-spatial dynamics within and across systems.…”

“…Several wild animal studies have suggested saturating nonlinear relationships between density and social association rates [8][9][10]13]. Such relationships imply that association rates do not increase passively with density, and that behavioural or demographic processes likely change as density increases, with the ultimate consequence of slowing association rates.…”